text: """   We have a sequence of books: the i-th book has thickness books[i][0] and
     height books[i][1].
     
     We want to place these books in order onto bookcase shelves that have total
     width shelf_width.
     
     We choose some of the books to place on this shelf (such that the sum of
     their thickness is <= shelf_width), then build another level of shelf of the
     bookcase so that the total height of the bookcase has increased by the
     maximum height of the books we just put down. We repeat this process until
     there are no more books to place.
     
     Note again that at each step of the above process, the order of the books we
     place is the same order as the given sequence of books. For example, if we
     have an ordered list of 5 books, we might place the first and second book
     onto the first shelf, the third book on the second shelf, and the fourth and
     fifth book on the last shelf.
     
     Return the minimum possible height that the total bookshelf can be after
     placing shelves in this manner.
     
     Input: books = [[1,1],[2,3],[2,3],[1,1],[1,1],[1,1],[1,2]], shelf_width = 4
     Output: 6
     
     Explanation: The sum of the heights of the 3 shelves are 1 + 3 + 2 = 6.
     Notice that book number 2 does not have to be on the first shelf.
     
     IDEA: 1) add books until possible tracking for each book the state of the
     shelf 2) when the shelf is full, true to put some books from the 1st shelf to
     the 2nd one if this helps to decrease the height 3) update the total height
     and repeat
     
     
     State diagrammer:
     
     
     [1,1],[2,3],  h = 3 
     [2,3]         h = 3
     
     [1,1],        h = 1 
     [2,3],[2,3]   h = 3
     
     
     [1,1],         h = 1 
     [2,3],[2,3],   h = 3 
     [1,1]          h = 1
     
     
     [1,1], 
     [2,3],[2,3], 
     [1,1],[1,1],[1,1],[1,2]
     
     
     IDEA:
     1) add book
     2) execute the back-processing for the deep up to shelfWidth
    
  """
  
  class Solution1105:
      pass
  